I am using Teams Desktop app for Windows and I have also access to the Web app.
Our customer has invited me to a team in their own account. She has used my organization's email address firstname.lastname@example.org. When I look into the forums, they talk of an option on the left side of my user icon to change the organization. But I see this option on neither Web nor desktop. I check with my colleague who uses the app on her Mac and she's able to switch, but not me.
Today, our customer sent a new invitation. I was logged out of the app to see whether I get to log in to the new organization and this is the message I get: